Some great examples and libs presented in this thread, but they didn't quite have what I was looking for. My approach: angular-validity -- a promise based validation lib for asynchronous validation, with optional Bootstrap styling baked-in.
An angular-validity solution for the OP's use case might look something like this:
<input type="text" name="field4" ng-model="field4"
validity="eval"
validity-eval="!(field1 && field2 && field3 && !field4)"
validity-message-eval="This field is required">
Here's a Fiddle, if you want to take it for a spin. The lib is available on GitHub, has detailed documentation, and plenty of live demos.